Problem: Simplify the expression. $(-2r^{4}+3r^{3}-4r^{2})(7r^{3}-4r)$
Explanation: First use the distributive property. $ - 2 r^4 (7 r^3) - 2 r^4 (-4 r) + 3 r^3 (7 r^3) + 3 r^3 (-4 r) - 4 r^2 (7 r^3) - 4 r^2 (-4 r) $ Simplify. $ - 14r^{7} + 8r^{5} + 21r^{6} - 12r^{4} - 28r^{5} + 16r^{3} $ $-14r^{7}+21r^{6}-20r^{5}-12r^{4}+16r^{3}$ Identify like terms. $ {- 14r^{7}} {+ 8r^{5}} {+ 21r^{6}} {- 12r^{4}} {- 28r^{5}} {+ 16r^{3}} $ Add the coefficients. $ { -14r^{7}} {+ 21r^{6}} { -20r^{5}} { -12r^{4}} {+ 16r^{3}} $